

A280118


Number of n X 2 0..2 arrays with no element unequal to a strict majority of its horizontal, vertical and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.


1



0, 4, 8, 28, 80, 252, 776, 2356, 7200, 21836, 66104, 199652, 601424, 1808252, 5426024, 16253460, 48608384, 145152940, 432853144, 1289129028, 3834701744, 11394112476, 33820033480, 100286009972, 297101633248, 879410116620, 2600884035320
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


LINKS

R. H. Hardin, Table of n, a(n) for n = 1..210


FORMULA

Empirical: a(n) = 2*a(n1) + 7*a(n2)  24*a(n4)  32*a(n5)  16*a(n6) for n>8.
Empirical g.f.: 4*x^2*(1  4*x^2  8*x^3  2*x^4 + 8*x^5 + 8*x^6) / (1  x  4*x^2  4*x^3)^2.  Colin Barker, Feb 12 2019


EXAMPLE

Some solutions for n=4:
..0..1. .0..0. .0..0. .0..0. .0..0. .0..0. .0..0. .0..0. .0..0. .0..0
..1..1. .1..0. .0..0. .0..1. .0..1. .0..1. .0..1. .0..1. .0..0. .1..1
..1..0. .0..0. .0..0. .2..2. .1..1. .1..1. .0..0. .1..1. .0..0. .1..1
..0..0. .0..0. .0..1. .2..2. .1..0. .2..1. .0..0. .1..2. .1..1. .1..1


CROSSREFS

Column 2 of A280124.
Sequence in context: A189546 A059480 A105723 * A143555 A025234 A075308
Adjacent sequences: A280115 A280116 A280117 * A280119 A280120 A280121


KEYWORD

nonn


AUTHOR

R. H. Hardin, Dec 26 2016


STATUS

approved



